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Joint Entrance Examination
Mathematics
Probability
Question 227
Question 227 of 417
Medium
MCQ
A candidate solves each of 50 problems correctly with probability
4
5
\dfrac45
5
4
. Find the probability he is unable to solve fewer than 2 problems (i.e., solves 49 or 50).
A
201
5
(
1
5
)
49
\dfrac{201}{5}\left(\dfrac15\right)^{49}
5
201
(
5
1
)
49
B
316
25
(
4
5
)
48
\dfrac{316}{25}\left(\dfrac45\right)^{48}
25
316
(
5
4
)
48
C
54
5
(
4
5
)
49
\dfrac{54}{5}\left(\dfrac45\right)^{49}
5
54
(
5
4
)
49
D
164
25
(
1
5
)
48
\dfrac{164}{25}\left(\dfrac15\right)^{48}
25
164
(
5
1
)
48
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Official solution
\[P = {}^{50}C_{50}p^{50}+{}^{50}C_{49}p^{49}q = p^{49}(p+50q) = \left(\frac45\right)^{49}\left(\frac45+10\right) = \frac{54}{5}\left(\frac45\right)^{49}\]
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